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Approximate of solution of a fourth order ordinary differential equations via tenth step block method. (English) Zbl 1453.65193

Summary: This paper carries a different approach of collection and interpolation to develop a tenth block method for the numerical solution of linear or nonlinear ordinary differential equations of fourth order with initial conditions. The method has been implemented at the selected mesh points to generate a direct tenth block method through Taylor series. Some critical properties of this method such as zero stability, order of the method, and convergence have been analysed. Two numerical tests have taken to make a comparison of the approximate results with exact as well as results of other authors.

MSC:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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